<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<meta name="generator" content="Doxygen 1.9.1"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>Calico: calico/bspline.hpp Source File</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<link href="search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="search/searchdata.js"></script>
<script type="text/javascript" src="search/search.js"></script>
<script type="text/x-mathjax-config">
  MathJax.Hub.Config({
    extensions: ["tex2jax.js"],
    jax: ["input/TeX","output/HTML-CSS"],
});
</script>
<script type="text/javascript" async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js"></script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
 <tbody>
 <tr style="height: 56px;">
  <td id="projectalign" style="padding-left: 0.5em;">
   <div id="projectname">Calico
   </div>
   <div id="projectbrief">A visual-inertial calibration library designed for rapid problem construction and debugging.</div>
  </td>
 </tr>
 </tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.9.1 -->
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
var searchBox = new SearchBox("searchBox", "search",false,'Search','.html');
/* @license-end */
</script>
<script type="text/javascript" src="menudata.js"></script>
<script type="text/javascript" src="menu.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
$(function() {
  initMenu('',true,false,'search.php','Search');
  $(document).ready(function() { init_search(); });
});
/* @license-end */</script>
<div id="main-nav"></div>
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
     onmouseover="return searchBox.OnSearchSelectShow()"
     onmouseout="return searchBox.OnSearchSelectHide()"
     onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>

<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<iframe src="javascript:void(0)" frameborder="0" 
        name="MSearchResults" id="MSearchResults">
</iframe>
</div>

<div id="nav-path" class="navpath">
  <ul>
<li class="navelem"><a class="el" href="dir_e7ac338090e46d594d3ea7a0e9efc7ba.html">calico</a></li>  </ul>
</div>
</div><!-- top -->
<div class="header">
  <div class="headertitle">
<div class="title">bspline.hpp</div>  </div>
</div><!--header-->
<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#include &lt;algorithm&gt;</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160; </div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="preprocessor">#include &quot;calico/statusor_macros.h&quot;</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#include &quot;ceres/problem.h&quot;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160; </div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespacecalico.html">calico</a> {</div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160; </div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160; </div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> N, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="keywordtype">int</span> BSpline&lt;N, T&gt;::AddParametersToProblem(ceres::Problem&amp; problem) {</div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;  <span class="keywordtype">int</span> num_parameters_added = 0;</div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;  <span class="keywordflow">for</span> (Eigen::Vector&lt;T, N&gt;&amp; control_point : control_points_) {</div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;    problem.AddParameterBlock(control_point.data(), control_point.size());</div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;    num_parameters_added += control_point.size();</div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;  }</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;  <span class="keywordflow">return</span> num_parameters_added;</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;}</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160; </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> N, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;absl::Status BSpline&lt;N, T&gt;::FitToData(</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;    <span class="keyword">const</span> std::vector&lt;T&gt;&amp; time,</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;    <span class="keyword">const</span> std::vector&lt;Eigen::Vector&lt;T,N&gt;&gt;&amp; data, <span class="keywordtype">int</span> spline_order,</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;    T knot_frequency) {</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;  RETURN_IF_ERROR(</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;      CheckDataForSplineFit(time, data, spline_order, knot_frequency));</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;  time_ = time;</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;  data_ = data;</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;  spline_order_ = spline_order;</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;  knot_frequency_ = knot_frequency;</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;  <span class="comment">// Derived information about the spline.</span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;  spline_degree_ = spline_order_ - 1;</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;  ComputeKnotVector();</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;  ComputeBasisMatrices();</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;  <span class="comment">// Fit the spline.</span></div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;  FitSpline();</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;  <span class="keywordflow">return</span> absl::OkStatus();</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;}</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160; </div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">int</span> N, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;Eigen::Vector&lt;T, N&gt; BSpline&lt;N, T&gt;::Evaluate(</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="keyword">const</span> Eigen::Ref&lt;<span class="keyword">const</span> Eigen::MatrixX&lt;T&gt;&gt;&amp; control_points_set, T knot0,</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;    T knot1, <span class="keyword">const</span> Eigen::MatrixX&lt;T&gt;&amp; basis_matrix, T stamp,</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;    <span class="keywordtype">int</span> derivative) {</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;  <span class="comment">// Compute u.</span></div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;  <span class="keyword">const</span> T dt = knot1 - knot0;</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;  <span class="keyword">const</span> T dt_inv = <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(1.0) / dt;</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;  <span class="keyword">const</span> T u = (stamp - knot0) * dt_inv;</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;  <span class="comment">// Derivative of u with respect to t raised to n&#39;th derivative power per</span></div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;  <span class="comment">// chain rule.</span></div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;  T dnu_dtn = <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(1.0);</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; derivative; ++j) {</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;    dnu_dtn *= dt_inv;</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;  }</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;  <span class="comment">// Construct U vector.</span></div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;  Eigen::Matrix&lt;T, 1, Eigen::Dynamic&gt; derivative_coeffs(</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;      control_points_set.rows());</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;  derivative_coeffs.setOnes();</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;  derivative_coeffs.head(derivative).setZero();</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;  Eigen::Matrix&lt;T, 1, Eigen::Dynamic&gt; U(control_points_set.rows());</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;  U.setOnes();</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = derivative; i &lt; derivative_coeffs.size(); ++i) {</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;    T coeff = <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(1.0);</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i - derivative; j &lt; i; ++j) {</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;      coeff *= (j + 1);</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    }</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    derivative_coeffs(i) = coeff;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    U(i) = (i &gt; derivative) ? (u * U(i-1)) : U(i);</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;  }</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;  U = U.array() * derivative_coeffs.array() * dnu_dtn;</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;  <span class="comment">// Evaluate spline.</span></div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;  <span class="keywordflow">return</span> (U * basis_matrix * control_points_set).transpose();</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;}</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160; </div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> N, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;absl::StatusOr&lt;std::vector&lt;Eigen::Vector&lt;T, N&gt;&gt;&gt; BSpline&lt;N, T&gt;::Interpolate(</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;    <span class="keyword">const</span> std::vector&lt;T&gt;&amp; times, <span class="keywordtype">int</span> derivative)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;  <span class="keywordflow">if</span> (derivative &lt; 0 || derivative &gt; spline_degree_) {</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    <span class="keywordflow">return</span> absl::InvalidArgumentError(<span class="stringliteral">&quot;Invalid derivative for interpolation.&quot;</span>);</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;  }</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;  <span class="keywordflow">for</span> (<span class="keyword">const</span> T&amp; t : times) {</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;    <span class="keywordflow">if</span> (t &lt; valid_knots_.front() || t &gt; valid_knots_.back()) {</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;      <span class="keywordflow">return</span> absl::InvalidArgumentError(absl::StrCat(</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;          <span class="stringliteral">&quot;Cannot interpolate &quot;</span>, t, <span class="stringliteral">&quot;. Value is not within valid knots.&quot;</span>));</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;    }</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;  }</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;  <span class="keywordtype">int</span> num_interp = times.size();</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;  std::vector&lt;Eigen::Vector&lt;T, N&gt;&gt; y(num_interp);</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; num_interp; ++i) {</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> spline_idx = GetSplineIndex(times.at(i));</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> knot_idx = GetKnotIndexFromSplineIndex(spline_idx);</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    <span class="keyword">const</span> Eigen::MatrixX&lt;T&gt; UM = GetSplineBasis(spline_idx, times.at(i), derivative);</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;    Eigen::MatrixX&lt;T&gt; control_points(spline_order_, N);</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; spline_order_; ++j) {</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;      control_points.row(j) = control_points_.at(spline_idx + j).transpose();</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    }</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    y[i] = Evaluate(control_points, knots_[knot_idx], knots_[knot_idx + 1],</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;                    Mi_[spline_idx], times[i], derivative);</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;  }</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;  <span class="keywordflow">return</span> y;</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;}</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160; </div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> N, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;Eigen::MatrixX&lt;T&gt; BSpline&lt;N, T&gt;::GetSplineBasis(</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;    <span class="keywordtype">int</span> spline_idx, T stamp, <span class="keywordtype">int</span> derivative)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;  <span class="comment">// Compute u.</span></div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> knot_idx = GetKnotIndexFromSplineIndex(spline_idx);</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;  <span class="keyword">const</span> T&amp; knot0 = knots_.at(knot_idx);</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;  <span class="keyword">const</span> T&amp; knot1 = knots_.at(knot_idx + 1);</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;  <span class="keyword">const</span> T dt = knot1 - knot0;</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;  <span class="keyword">const</span> T dt_inv = <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(1.0) / dt;</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;  <span class="keyword">const</span> T u = (stamp - knot0) * dt_inv;</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;  <span class="comment">// Derivative of u with respect to t raised to n&#39;th derivative power per</span></div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;  <span class="comment">// chain rule.</span></div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;  T dnu_dtn = <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(1.0);</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; derivative; ++j) {</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    dnu_dtn *= dt_inv;</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;  }</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;  <span class="comment">// Construct U vector.</span></div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;  Eigen::Matrix&lt;T, 1, Eigen::Dynamic&gt; derivative_coeffs(spline_order_);</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;  derivative_coeffs.setOnes();</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;  derivative_coeffs.head(derivative).setZero();</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;  Eigen::Matrix&lt;T, 1, Eigen::Dynamic&gt; U(spline_order_);</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;  U.setOnes();</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = derivative; i &lt; derivative_coeffs.size(); ++i) {</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    T coeff = <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(1.0);</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i - derivative; j &lt; i; ++j) {</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;      coeff *= (j + 1);</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;    }</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;    derivative_coeffs(i) = coeff;</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;    U(i) = (i &gt; derivative) ? (u * U(i-1)) : U(i);</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;  }</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;  U = U.array() * derivative_coeffs.array() * dnu_dtn;</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;  <span class="keyword">const</span> Eigen::MatrixX&lt;T&gt;&amp; basis_matrix = Mi_.at(spline_idx);</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;  <span class="keywordflow">return</span> U * basis_matrix;</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;}</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160; </div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160; </div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> N, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;<span class="keywordtype">int</span> BSpline&lt;N, T&gt;::GetSplineIndex(T query_time)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;  <span class="keywordtype">int</span> spline_idx = -1;</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;  <span class="keywordflow">if</span> (query_time == valid_knots_.back()) {</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;    spline_idx = valid_knots_.size() - 2;</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;  }</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (query_time &lt; valid_knots_.back()) {</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;    <span class="keyword">auto</span> lower =</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;      std::upper_bound(valid_knots_.begin(), valid_knots_.end(), query_time);</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;    spline_idx = lower - valid_knots_.begin() - 1;</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;  }</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;  <span class="keywordflow">return</span> spline_idx;</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;}</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160; </div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> N, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;<span class="keywordtype">int</span> BSpline&lt;N, T&gt;::GetSplineOrder()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;  <span class="keywordflow">return</span> spline_order_;</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;}</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160; </div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> N, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;<span class="keywordtype">int</span> BSpline&lt;N, T&gt;::GetKnotIndexFromSplineIndex(</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    <span class="keywordtype">int</span> control_point_index)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;  <span class="keywordflow">return</span> control_point_index + spline_degree_;</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;}</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160; </div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> N, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;<span class="keywordtype">void</span> BSpline&lt;N, T&gt;::ComputeKnotVector() {</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;  <span class="keyword">const</span> T duration = time_.back() - time_.front();</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;  <span class="keyword">const</span> T dt = 1.0 / knot_frequency_;</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> num_valid_knots = 1 + std::ceil(duration * knot_frequency_);</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> num_knots = num_valid_knots + 2 * spline_degree_;</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160; </div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;  knots_.resize(num_knots);</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;  valid_knots_.resize(num_valid_knots);</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = -spline_degree_; i &lt; num_knots - spline_degree_; ++i) {</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;    <span class="keyword">const</span> T knot_value = time_.front() + dt * i;</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;    knots_[i + spline_degree_] = knot_value;</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    <span class="keywordtype">int</span> valid_knot_index = i;</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    <span class="keywordflow">if</span> (valid_knot_index &gt; -1 &amp;&amp; valid_knot_index &lt; num_valid_knots) {</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;      valid_knots_[valid_knot_index] = knot_value;</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    }</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;  }</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;}</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160; </div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> N, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;<span class="keywordtype">void</span> BSpline&lt;N, T&gt;::ComputeBasisMatrices() {</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> num_valid_segments = valid_knots_.size() - 1;</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;  Mi_.resize(num_valid_segments);</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; num_valid_segments; ++i) {</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;    Mi_[i] = M(spline_order_, i + spline_degree_);</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;  }</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;}</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160; </div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">int</span> N, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;Eigen::MatrixX&lt;T&gt; BSpline&lt;N, T&gt;::M(<span class="keywordtype">int</span> k, <span class="keywordtype">int</span> i) {</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;  Eigen::MatrixX&lt;T&gt; M_k;</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;  <span class="keywordflow">if</span> (k == 1) {</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;    M_k.resize(k, k);</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;    M_k(0, 0) = k;</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;    <span class="keywordflow">return</span> M_k;</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;  }</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160; </div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;  Eigen::MatrixX&lt;T&gt; M_km1 = M(k - 1, i);</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> num_rows = M_km1.rows();</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> num_cols = M_km1.cols();</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;  Eigen::MatrixX&lt;T&gt; M1(num_rows + 1, num_cols), M2(num_rows + 1, num_cols);</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;  M1.setZero();</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;  M2.setZero();</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;  M1.block(0, 0, num_rows, num_cols) = M_km1;</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;  M2.block(1, 0, num_rows, num_cols) = M_km1;</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160; </div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;  Eigen::MatrixX&lt;T&gt; A(k - 1,k);</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;  Eigen::MatrixX&lt;T&gt; B(k - 1,k);</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;  A.setZero();</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;  B.setZero();</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> index = 0; index &lt; k - 1; ++index) {</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;    <span class="keywordtype">int</span> j = i - k + 2 + index;</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;    <span class="keyword">const</span> T d0 = d_0(k, i, j);</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;    <span class="keyword">const</span> T d1 = d_1(k, i, j);</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;    A(index, index) = 1.0 - d0;</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;    A(index, index + 1) = d0;</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;    B(index, index) = -d1;</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    B(index, index + 1) = d1;</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;  }</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;  M_k = M1 * A + M2 * B;</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;  <span class="keywordflow">return</span> M_k;</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;}</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160; </div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> N, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;T BSpline&lt;N, T&gt;::d_0(<span class="keywordtype">int</span> k, <span class="keywordtype">int</span> i, <span class="keywordtype">int</span> j) {</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;  <span class="keyword">const</span> T den = knots_[j + k - 1] - knots_[j];</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;  <span class="keywordflow">if</span> (den &lt;= 0.0) {</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;    <span class="keywordflow">return</span> 0.0;</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;  }</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;  <span class="keyword">const</span> T num = knots_[i] - knots_[j];</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;  <span class="keywordflow">return</span> num / den;</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;}</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160; </div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> N, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;T BSpline&lt;N, T&gt;::d_1(<span class="keywordtype">int</span> k, <span class="keywordtype">int</span> i, <span class="keywordtype">int</span> j) {</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;  <span class="keyword">const</span> T den = knots_[j + k - 1] - knots_[j];</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;  <span class="keywordflow">if</span> (den &lt;= 0.0) {</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;    <span class="keywordflow">return</span> 0.0;</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;  }</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;  <span class="keyword">const</span> T num = knots_[i+1] - knots_[i];</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;  <span class="keywordflow">return</span> num / den;</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;}</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160; </div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> N, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;<span class="keywordtype">void</span> BSpline&lt;N, T&gt;::FitSpline() {</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> num_data = time_.size();</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;  <span class="keywordtype">int</span> num_control_points = knots_.size() - spline_order_;</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;  Eigen::MatrixX&lt;T&gt; X(num_data, num_control_points);</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;  X.setZero();</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; num_data; j++) {</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;    <span class="keyword">const</span> T t = time_[j];</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;    <span class="keywordtype">int</span> spline_index = -1;</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160; </div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;    <span class="keywordflow">if</span> (t == valid_knots_.back()) {</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;      spline_index = Mi_.size() - 1;</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;    }</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (t == valid_knots_.front()) {</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;      spline_index = 0;</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;    }</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (t &lt; valid_knots_.back()) {</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;      <span class="keyword">auto</span> lower = std::upper_bound(valid_knots_.begin(), valid_knots_.end(), t);</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;      spline_index = lower - valid_knots_.begin() - 1;</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;    }</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">int</span> knot_index = GetKnotIndexFromSplineIndex(spline_index);</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;    <span class="comment">// Grab the intermediate knot values</span></div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;    <span class="keyword">const</span> T ti = knots_[knot_index];</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;    <span class="keyword">const</span> T tii = knots_[knot_index + 1];</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;    <span class="comment">// Construct U vector</span></div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;    Eigen::VectorX&lt;T&gt; U(spline_order_);</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;    U.setOnes();</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;    <span class="keyword">const</span> T u = (t - ti) / (tii - ti);</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt; spline_order_; ++i) {</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;      U(i) = u * U(i - 1);</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;    }</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;    <span class="comment">// Construct U*M</span></div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;    Eigen::MatrixX&lt;T&gt; M = Mi_[spline_index];</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;    Eigen::MatrixX&lt;T&gt; UM = U.transpose() * M;</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;    X.block(j, spline_index, UM.rows(), UM.cols()) = UM;</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;  }</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160; </div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;  Eigen::Matrix&lt;T,Eigen::Dynamic,N&gt; data(num_data, N);</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; num_data; ++i) {</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;    data.row(i) = data_[i].transpose();</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;  }</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;  <span class="comment">// TODO(yangjames): X is highly sparse, and X&#39;X is banded, symmetric, positive</span></div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;  <span class="comment">// definite. Figure out how to sparsify the solve step for the control points</span></div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;  <span class="comment">// as this gets very expensive with more knots.</span></div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;  <span class="keyword">const</span> Eigen::MatrixX&lt;T&gt; XtX = X.transpose() * X;</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;  <span class="keyword">const</span> Eigen::MatrixX&lt;T&gt; Xtd = X.transpose() * data;</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;  <span class="keyword">const</span> Eigen::MatrixX&lt;T&gt; control_points =</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;      XtX.colPivHouseholderQr().solve(Xtd);</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; control_points.rows(); ++i) {</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;    control_points_.push_back(control_points.row(i).transpose());</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;  }</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;}</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160; </div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> N, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;absl::Status BSpline&lt;N, T&gt;::CheckDataForSplineFit(</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;    <span class="keyword">const</span> std::vector&lt;T&gt;&amp; time,</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;    <span class="keyword">const</span> std::vector&lt;Eigen::Vector&lt;T, N&gt;&gt;&amp; data,</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;    <span class="keywordtype">int</span> spline_order, T knot_frequency) {</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;  <span class="comment">// Assert that data and time are properly sized</span></div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;  <span class="keywordflow">if</span> (!time.size()) {</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;    <span class="keywordflow">return</span> absl::InvalidArgumentError(<span class="stringliteral">&quot;Attempted to fit data on empty time vector.&quot;</span>);</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;  }</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;  <span class="keywordflow">if</span> (data.empty()) {</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;    <span class="keywordflow">return</span> absl::InvalidArgumentError(<span class="stringliteral">&quot;Attempted to fit on empty data.&quot;</span>);</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;  }</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;  <span class="keywordflow">if</span> (time.size() != data.size()) {</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;    <span class="keywordflow">return</span> absl::InvalidArgumentError(<span class="stringliteral">&quot;Data and time vectors are not the same size.&quot;</span>);</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;  }</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;  <span class="comment">// Check that time is strictly increasing</span></div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;  <span class="keyword">auto</span> iter = std::adjacent_find(time_.begin(), time_.end(), std::greater&lt;T&gt;());</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;  <span class="keywordflow">if</span> (iter != time_.end()) {</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;    <span class="keywordflow">return</span> absl::InvalidArgumentError(<span class="stringliteral">&quot;Time vector is not monotonically increasing.&quot;</span>);</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;  }</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;  <span class="comment">// Check that spline order is greater than 2</span></div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;  <span class="keywordflow">if</span> (spline_order &lt; 2) {</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;    <span class="keywordflow">return</span> absl::InvalidArgumentError(absl::StrCat(</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;        <span class="stringliteral">&quot;Spline order must be greater than 2. Got &quot;</span>, spline_order));</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;  }</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;  <span class="comment">// Check that knot frequency is greater than 0</span></div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;  <span class="keywordflow">if</span> (knot_frequency &lt;= 0) {</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;    <span class="keywordflow">return</span> absl::InvalidArgumentError(<span class="stringliteral">&quot;Knot frequency must be greater than 0.&quot;</span>);</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;  }</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;  <span class="keywordflow">return</span> absl::OkStatus();</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;}</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160; </div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;} <span class="comment">// namespace calico</span></div>
<div class="ttc" id="anamespacecalico_html"><div class="ttname"><a href="namespacecalico.html">calico</a></div><div class="ttdoc">Primary calico namespace.</div><div class="ttdef"><b>Definition:</b> __init__.py:1</div></div>
</div><!-- fragment --></div><!-- contents -->
<!-- start footer part -->
<hr class="footer"/><address class="footer"><small>
Generated by&#160;<a href="https://www.doxygen.org/index.html"><img class="footer" src="doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.1
</small></address>
</body>
</html>
